The second data release from the European Pulsar Timing Array: II. Customised pulsar noise models for spatially correlated gravitational waves

Aims. The nanohertz gravitational wave background (GWB) is expected to be an aggregate signal of an ensemble of gravitational waves emitted predominantly by a large population of coalescing supermassive black hole binaries in the centres of merging galaxies. Pulsar timing arrays (PTAs), which are ensembles of extremely stable pulsars at approximately kiloparsec distances precisely monitored for decades, are the most precise experiments capable of detecting this background. However, the subtle imprints that the GWB induces on pulsar timing data are obscured by many sources of noise that occur on various timescales. These must be carefully modelled and mitigated to increase the sensitivity to the background signal. Methods. In this paper, we present a novel technique to estimate the optimal number of frequency coefficients for modelling achromatic and chromatic noise, while selecting the preferred set of noise models to use for each pulsar. We also incorporated a new model to fit for scattering variations in the Bayesian pulsar timing package temponest. These customised noise models enable a more robust characterisation of single-pulsar noise. We developed a software package based on tempo2 to create realistic simulations of European Pulsar Timing Array (EPTA) datasets that allowed us to test the efficacy of our noise modelling algorithms. Results. Using these techniques, we present an in-depth analysis of the noise properties of 25 millisecond pulsars (MSPs) that form the second data release (DR2) of the EPTA and investigate the effect of incorporating low-frequency data from the Indian Pulsar Timing Array collaboration for a common sample of ten MSPs. We used two packages, enterprise and temponest, to estimate our noise models and compare them with those reported using EPTA DR1. We find that, while in some pulsars we can successfully disentangle chromatic from achromatic noise owing to the wider frequency coverage in DR2, in others the noise models evolve in a much more complicated way. We also find evidence of long-term scattering variations in PSR J1600-3053. Through our simulations, we identify intrinsic biases in our current noise analysis techniques and discuss their effect on GWB searches. The analysis and results discussed in this article directly help to improve the sensitivity to the GWB signal and they are already being used as part of global PTA efforts.